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01 Aug 2022, 02:20
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
57% (01:58) correct
43%
(02:05)
wrong
based on 204
sessions
History
Date
Time
Result
Not Attempted Yet
In how many ways can the letters of the word MACHINE be arranged so that the vowels may occupy only odd position?
(A) 20160
(B) 576
(C) 288
(D) 144
(E) 72
Are You Up For the Challenge: 700 Level Questions
(A) 20160
(B) 576
(C) 288
(D) 144
(E) 72
Are You Up For the Challenge: 700 Level Questions
NCC
Joined: 20 Aug 2018
Last visit: 07 Sep 2024
Posts: 180
Given Kudos: 295
Location: India
Schools: Goizueta '25 (D) Foster '25 (D) Marshall '25 (D) McCombs '25 (D) McDonough '25 (WL) Mendoza '25 (D) NUS (D) ISB '24 (D) Kelley '25 (A$$$) Kenan-Flagler '25 (A$$) Owen '25 (D) Cox (II) Rice Jones '25 (D) Tepper '25 (WL) IMD Jan'24 intake (A$) Rotman '25 (II)
GMAT 1: 640 Q48 V28
GMAT 2: 610 Q47 V27
GPA: 3.42
01 Aug 2022, 03:23
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Solution:
M A C H I N E
3 vowels - A I E
_1_ _2_ _3_ _4_ _5_ _6_ _7_
1] arranging vowels at 4 odd places = 4C3 X 3!
2] arrange the consonants = 4!
AND operator used
= 4C3 X 3! X 4!
=576
Option B
M A C H I N E
3 vowels - A I E
_1_ _2_ _3_ _4_ _5_ _6_ _7_
1] arranging vowels at 4 odd places = 4C3 X 3!
2] arrange the consonants = 4!
AND operator used
= 4C3 X 3! X 4!
=576
Option B
01 Aug 2022, 04:54
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Bookmarks
Total vowels = 3(A, I, and E)
Total words = 7
Thus, there are 4 odd places.
3 vowels can be arranged on 4 odd places in 4*3! ways = 24
4 consonants can be arranged in 4! ways.
Thus, total ways = 4!*24 = 576
Thus the correct answer is B.
Total words = 7
Thus, there are 4 odd places.
3 vowels can be arranged on 4 odd places in 4*3! ways = 24
4 consonants can be arranged in 4! ways.
Thus, total ways = 4!*24 = 576
Thus the correct answer is B.
